A research study was ocnducted to determine the objective response rate and toxicities associated with Bryostatin-1 in a group of patients who had chronic myelogenous leukemia for which standard forms of treatment including chemotherapy or bone marrow transplant are ineffective or are not generally thought to offer a likelihood of curative benefit. Two patients were entered into the study to determine response rate, evaluate side effects, look for evidence that the drug had effectiveness in this disease and to measure the amount of drug present in the blood at various times following administration. The study was also designed to look at the effect of the drug on bone marrow cells, tumor cells in the blood, normal blood cells and the production of certain proteins produced in the body and to learn more about the biologic effects of Bryostatin-1 and how it works in humans. The investigators left UAB following the enrollment of the first two patients and the study has been closed.